Question: Michael is 28 years older than Luis. Seventeen years ago, Michael was 5 times as old as Luis. How old is Luis now?
Answer: We can use the given information to write down two equations that describe the ages of Michael and Luis. Let Michael's current age be $m$ and Luis's current age be $l$ The information in the first sentence can be expressed in the following equation: $m = l + 28$ Seventeen years ago, Michael was $m - 17$ years old, and Luis was $l - 17$ years old. The information in the second sentence can be expressed in the following equation: $m - 17 = 5(l - 17)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $l$ , it might be easiest to use our first equation for $m$ and substitute it into our second equation. Our first equation is: $m = l + 28$ . Substituting this into our second equation, we get the equation: $(l + 28)$ $-$ $17 = 5(l - 17)$ which combines the information about $l$ from both of our original equations. Simplifying both sides of this equation, we get: $l + 11 = 5 l - 85$ Solving for $l$ , we get: $4 l = 96$ $l = 24$.